TSTP Solution File: LCL206-3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL206-3 : TPTP v8.1.0. Bugfixed v2.4.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:50:36 EDT 2022
% Result : Unsatisfiable 261.84s 262.04s
% Output : CNFRefutation 261.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 33
% Syntax : Number of clauses : 199 ( 106 unt; 0 nHn; 85 RR)
% Number of literals : 323 ( 90 equ; 125 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 466 ( 42 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
axiom(implies(or(A,A),A)) ).
cnf(axiom_1_3,axiom,
axiom(implies(A,or(B,A))) ).
cnf(axiom_1_4,axiom,
axiom(implies(or(A,B),or(B,A))) ).
cnf(axiom_1_5,axiom,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ).
cnf(axiom_1_6,axiom,
axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) ).
cnf(implies_definition,axiom,
implies(X,Y) = or(not(X),Y) ).
cnf(rule_1,axiom,
( theorem(X)
| ~ axiom(X) ) ).
cnf(rule_2,axiom,
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ) ).
cnf(prove_this,negated_conjecture,
~ theorem(implies(not(implies(p,q)),implies(not(p),not(q)))) ).
cnf(refute_0_0,plain,
( ~ theorem(implies(implies(not(not(or(X_22111,not(X_22111)))),X_22112),X_22112))
| ~ theorem(implies(not(not(or(X_22111,not(X_22111)))),X_22112))
| theorem(X_22112) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_22112)),bind(Y,$fot(implies(not(not(or(X_22111,not(X_22111)))),X_22112)))]]) ).
cnf(refute_0_1,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_2,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_1]) ).
cnf(refute_0_3,plain,
theorem(implies(or(X_67,X_67),X_67)),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_67))]]) ).
cnf(refute_0_4,plain,
( ~ theorem(implies(or(X_67,X_67),X_67))
| ~ theorem(or(X_67,X_67))
| theorem(X_67) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_67)),bind(Y,$fot(or(X_67,X_67)))]]) ).
cnf(refute_0_5,plain,
( ~ theorem(or(X_67,X_67))
| theorem(X_67) ),
inference(resolve,[$cnf( theorem(implies(or(X_67,X_67),X_67)) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ theorem(or(implies(X_157,X_157),implies(X_157,X_157)))
| theorem(implies(X_157,X_157)) ),
inference(subst,[],[refute_0_5:[bind(X_67,$fot(implies(X_157,X_157)))]]) ).
cnf(refute_0_7,plain,
( ~ axiom(implies(X_3,or(X_4,X_3)))
| theorem(implies(X_3,or(X_4,X_3))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(X_3,or(X_4,X_3))))]]) ).
cnf(refute_0_8,plain,
axiom(implies(X_3,or(X_4,X_3))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_3)),bind(B,$fot(X_4))]]) ).
cnf(refute_0_9,plain,
theorem(implies(X_3,or(X_4,X_3))),
inference(resolve,[$cnf( axiom(implies(X_3,or(X_4,X_3))) )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
theorem(implies(X_155,or(X_154,X_155))),
inference(subst,[],[refute_0_9:[bind(X_3,$fot(X_155)),bind(X_4,$fot(X_154))]]) ).
cnf(refute_0_11,plain,
( ~ axiom(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33))))
| theorem(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))))]]) ).
cnf(refute_0_12,plain,
axiom(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_31)),bind(B,$fot(X_32)),bind(C,$fot(X_33))]]) ).
cnf(refute_0_13,plain,
theorem(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))),
inference(resolve,[$cnf( axiom(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))) )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
theorem(implies(or(not(X),or(X_47,X_48)),or(X_47,or(not(X),X_48)))),
inference(subst,[],[refute_0_13:[bind(X_31,$fot(not(X))),bind(X_32,$fot(X_47)),bind(X_33,$fot(X_48))]]) ).
cnf(refute_0_15,plain,
implies(X,X_48) = or(not(X),X_48),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_48))]]) ).
cnf(refute_0_16,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_17,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_18,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( implies(X,X_48) != or(not(X),X_48)
| or(not(X),X_48) = implies(X,X_48) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(implies(X,X_48))),bind(Y0,$fot(or(not(X),X_48)))]]) ).
cnf(refute_0_20,plain,
or(not(X),X_48) = implies(X,X_48),
inference(resolve,[$cnf( $equal(implies(X,X_48),or(not(X),X_48)) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
( or(not(X),X_48) != implies(X,X_48)
| ~ theorem(implies(or(not(X),or(X_47,X_48)),or(X_47,or(not(X),X_48))))
| theorem(implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_47,X_48)),or(X_47,or(not(X),X_48)))) ),[0,1,1],$fot(implies(X,X_48))]]) ).
cnf(refute_0_22,plain,
( ~ theorem(implies(or(not(X),or(X_47,X_48)),or(X_47,or(not(X),X_48))))
| theorem(implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_48),implies(X,X_48)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
theorem(implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_47,X_48)),or(X_47,or(not(X),X_48)))) )],[refute_0_14,refute_0_22]) ).
cnf(refute_0_24,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_25,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_24]) ).
cnf(refute_0_26,plain,
or(not(X),or(X_47,X_48)) = implies(X,or(X_47,X_48)),
inference(subst,[],[refute_0_25:[bind(Y,$fot(or(X_47,X_48)))]]) ).
cnf(refute_0_27,plain,
implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48))) = implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48))))]]) ).
cnf(refute_0_28,plain,
( implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48))) != implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48)))
| or(not(X),or(X_47,X_48)) != implies(X,or(X_47,X_48))
| implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48))) = implies(implies(X,or(X_47,X_48)),or(X_47,implies(X,X_48))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48))),implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48)))) ),[1,0],$fot(implies(X,or(X_47,X_48)))]]) ).
cnf(refute_0_29,plain,
( or(not(X),or(X_47,X_48)) != implies(X,or(X_47,X_48))
| implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48))) = implies(implies(X,or(X_47,X_48)),or(X_47,implies(X,X_48))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48))),implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48)))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48))) = implies(implies(X,or(X_47,X_48)),or(X_47,implies(X,X_48))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_47,X_48)),implies(X,or(X_47,X_48))) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
( implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48))) != implies(implies(X,or(X_47,X_48)),or(X_47,implies(X,X_48)))
| ~ theorem(implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48))))
| theorem(implies(implies(X,or(X_47,X_48)),or(X_47,implies(X,X_48)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48)))) ),[0],$fot(implies(implies(X,or(X_47,X_48)),or(X_47,implies(X,X_48))))]]) ).
cnf(refute_0_32,plain,
( ~ theorem(implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48))))
| theorem(implies(implies(X,or(X_47,X_48)),or(X_47,implies(X,X_48)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48))),implies(implies(X,or(X_47,X_48)),or(X_47,implies(X,X_48)))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
theorem(implies(implies(X,or(X_47,X_48)),or(X_47,implies(X,X_48)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_47,X_48)),or(X_47,implies(X,X_48)))) )],[refute_0_23,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ theorem(implies(X,or(X_47,X_48)))
| ~ theorem(implies(implies(X,or(X_47,X_48)),or(X_47,implies(X,X_48))))
| theorem(or(X_47,implies(X,X_48))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_47,implies(X,X_48)))),bind(Y,$fot(implies(X,or(X_47,X_48))))]]) ).
cnf(refute_0_35,plain,
( ~ theorem(implies(X,or(X_47,X_48)))
| theorem(or(X_47,implies(X,X_48))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,or(X_47,X_48)),or(X_47,implies(X,X_48)))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ theorem(implies(X_155,or(X_154,X_155)))
| theorem(or(X_154,implies(X_155,X_155))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(X_155)),bind(X_47,$fot(X_154)),bind(X_48,$fot(X_155))]]) ).
cnf(refute_0_37,plain,
theorem(or(X_154,implies(X_155,X_155))),
inference(resolve,[$cnf( theorem(implies(X_155,or(X_154,X_155))) )],[refute_0_10,refute_0_36]) ).
cnf(refute_0_38,plain,
theorem(or(implies(X_157,X_157),implies(X_157,X_157))),
inference(subst,[],[refute_0_37:[bind(X_154,$fot(implies(X_157,X_157))),bind(X_155,$fot(X_157))]]) ).
cnf(refute_0_39,plain,
theorem(implies(X_157,X_157)),
inference(resolve,[$cnf( theorem(or(implies(X_157,X_157),implies(X_157,X_157))) )],[refute_0_38,refute_0_6]) ).
cnf(refute_0_40,plain,
theorem(implies(X_290,X_290)),
inference(subst,[],[refute_0_39:[bind(X_157,$fot(X_290))]]) ).
cnf(refute_0_41,plain,
( ~ axiom(implies(implies(X_17,X_18),or(X_18,not(X_17))))
| theorem(implies(implies(X_17,X_18),or(X_18,not(X_17)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_17,X_18),or(X_18,not(X_17)))))]]) ).
cnf(refute_0_42,plain,
axiom(implies(or(not(X),X_14),or(X_14,not(X)))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(not(X))),bind(B,$fot(X_14))]]) ).
cnf(refute_0_43,plain,
implies(X,X_14) = or(not(X),X_14),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_14))]]) ).
cnf(refute_0_44,plain,
( implies(X,X_14) != or(not(X),X_14)
| or(not(X),X_14) = implies(X,X_14) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(implies(X,X_14))),bind(Y0,$fot(or(not(X),X_14)))]]) ).
cnf(refute_0_45,plain,
or(not(X),X_14) = implies(X,X_14),
inference(resolve,[$cnf( $equal(implies(X,X_14),or(not(X),X_14)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( or(not(X),X_14) != implies(X,X_14)
| ~ axiom(implies(or(not(X),X_14),or(X_14,not(X))))
| axiom(implies(implies(X,X_14),or(X_14,not(X)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),X_14),or(X_14,not(X)))) ),[0,0],$fot(implies(X,X_14))]]) ).
cnf(refute_0_47,plain,
( ~ axiom(implies(or(not(X),X_14),or(X_14,not(X))))
| axiom(implies(implies(X,X_14),or(X_14,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_14),implies(X,X_14)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
axiom(implies(implies(X,X_14),or(X_14,not(X)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),X_14),or(X_14,not(X)))) )],[refute_0_42,refute_0_47]) ).
cnf(refute_0_49,plain,
axiom(implies(implies(X_17,X_18),or(X_18,not(X_17)))),
inference(subst,[],[refute_0_48:[bind(X,$fot(X_17)),bind(X_14,$fot(X_18))]]) ).
cnf(refute_0_50,plain,
theorem(implies(implies(X_17,X_18),or(X_18,not(X_17)))),
inference(resolve,[$cnf( axiom(implies(implies(X_17,X_18),or(X_18,not(X_17)))) )],[refute_0_49,refute_0_41]) ).
cnf(refute_0_51,plain,
( ~ theorem(implies(X_17,X_18))
| ~ theorem(implies(implies(X_17,X_18),or(X_18,not(X_17))))
| theorem(or(X_18,not(X_17))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_18,not(X_17)))),bind(Y,$fot(implies(X_17,X_18)))]]) ).
cnf(refute_0_52,plain,
( ~ theorem(implies(X_17,X_18))
| theorem(or(X_18,not(X_17))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_17,X_18),or(X_18,not(X_17)))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ theorem(implies(X_290,X_290))
| theorem(or(X_290,not(X_290))) ),
inference(subst,[],[refute_0_52:[bind(X_17,$fot(X_290)),bind(X_18,$fot(X_290))]]) ).
cnf(refute_0_54,plain,
theorem(or(X_290,not(X_290))),
inference(resolve,[$cnf( theorem(implies(X_290,X_290)) )],[refute_0_40,refute_0_53]) ).
cnf(refute_0_55,plain,
( ~ theorem(X_292)
| ~ theorem(implies(X_292,not(not(X_292))))
| theorem(not(not(X_292))) ),
inference(subst,[],[rule_2:[bind(X,$fot(not(not(X_292)))),bind(Y,$fot(X_292))]]) ).
cnf(refute_0_56,plain,
theorem(or(not(X),not(not(X)))),
inference(subst,[],[refute_0_54:[bind(X_290,$fot(not(X)))]]) ).
cnf(refute_0_57,plain,
implies(X,not(not(X))) = or(not(X),not(not(X))),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(not(X))))]]) ).
cnf(refute_0_58,plain,
( implies(X,not(not(X))) != or(not(X),not(not(X)))
| or(not(X),not(not(X))) = implies(X,not(not(X))) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(implies(X,not(not(X))))),bind(Y0,$fot(or(not(X),not(not(X)))))]]) ).
cnf(refute_0_59,plain,
or(not(X),not(not(X))) = implies(X,not(not(X))),
inference(resolve,[$cnf( $equal(implies(X,not(not(X))),or(not(X),not(not(X)))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( or(not(X),not(not(X))) != implies(X,not(not(X)))
| ~ theorem(or(not(X),not(not(X))))
| theorem(implies(X,not(not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X),not(not(X)))) ),[0],$fot(implies(X,not(not(X))))]]) ).
cnf(refute_0_61,plain,
( ~ theorem(or(not(X),not(not(X))))
| theorem(implies(X,not(not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(not(X))),implies(X,not(not(X)))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
theorem(implies(X,not(not(X)))),
inference(resolve,[$cnf( theorem(or(not(X),not(not(X)))) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
theorem(implies(X_292,not(not(X_292)))),
inference(subst,[],[refute_0_62:[bind(X,$fot(X_292))]]) ).
cnf(refute_0_64,plain,
( ~ theorem(X_292)
| theorem(not(not(X_292))) ),
inference(resolve,[$cnf( theorem(implies(X_292,not(not(X_292)))) )],[refute_0_63,refute_0_55]) ).
cnf(refute_0_65,plain,
( ~ theorem(or(X_290,not(X_290)))
| theorem(not(not(or(X_290,not(X_290))))) ),
inference(subst,[],[refute_0_64:[bind(X_292,$fot(or(X_290,not(X_290))))]]) ).
cnf(refute_0_66,plain,
theorem(not(not(or(X_290,not(X_290))))),
inference(resolve,[$cnf( theorem(or(X_290,not(X_290))) )],[refute_0_54,refute_0_65]) ).
cnf(refute_0_67,plain,
( ~ theorem(X_272)
| ~ theorem(implies(X_272,implies(implies(X_272,X_273),X_273)))
| theorem(implies(implies(X_272,X_273),X_273)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(implies(X_272,X_273),X_273))),bind(Y,$fot(X_272))]]) ).
cnf(refute_0_68,plain,
( ~ theorem(implies(or(X_47,X_48),or(X_47,X_48)))
| theorem(or(X_47,implies(or(X_47,X_48),X_48))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(or(X_47,X_48)))]]) ).
cnf(refute_0_69,plain,
theorem(implies(or(X_47,X_48),or(X_47,X_48))),
inference(subst,[],[refute_0_39:[bind(X_157,$fot(or(X_47,X_48)))]]) ).
cnf(refute_0_70,plain,
theorem(or(X_47,implies(or(X_47,X_48),X_48))),
inference(resolve,[$cnf( theorem(implies(or(X_47,X_48),or(X_47,X_48))) )],[refute_0_69,refute_0_68]) ).
cnf(refute_0_71,plain,
theorem(or(not(X),implies(or(not(X),X_203),X_203))),
inference(subst,[],[refute_0_70:[bind(X_47,$fot(not(X))),bind(X_48,$fot(X_203))]]) ).
cnf(refute_0_72,plain,
implies(X,X_203) = or(not(X),X_203),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_203))]]) ).
cnf(refute_0_73,plain,
( implies(X,X_203) != or(not(X),X_203)
| or(not(X),X_203) = implies(X,X_203) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(implies(X,X_203))),bind(Y0,$fot(or(not(X),X_203)))]]) ).
cnf(refute_0_74,plain,
or(not(X),X_203) = implies(X,X_203),
inference(resolve,[$cnf( $equal(implies(X,X_203),or(not(X),X_203)) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
( or(not(X),X_203) != implies(X,X_203)
| ~ theorem(or(not(X),implies(or(not(X),X_203),X_203)))
| theorem(or(not(X),implies(implies(X,X_203),X_203))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X),implies(or(not(X),X_203),X_203))) ),[0,1,0],$fot(implies(X,X_203))]]) ).
cnf(refute_0_76,plain,
( ~ theorem(or(not(X),implies(or(not(X),X_203),X_203)))
| theorem(or(not(X),implies(implies(X,X_203),X_203))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_203),implies(X,X_203)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
theorem(or(not(X),implies(implies(X,X_203),X_203))),
inference(resolve,[$cnf( theorem(or(not(X),implies(or(not(X),X_203),X_203))) )],[refute_0_71,refute_0_76]) ).
cnf(refute_0_78,plain,
or(not(X),implies(implies(X,X_203),X_203)) = implies(X,implies(implies(X,X_203),X_203)),
inference(subst,[],[refute_0_25:[bind(Y,$fot(implies(implies(X,X_203),X_203)))]]) ).
cnf(refute_0_79,plain,
( or(not(X),implies(implies(X,X_203),X_203)) != implies(X,implies(implies(X,X_203),X_203))
| ~ theorem(or(not(X),implies(implies(X,X_203),X_203)))
| theorem(implies(X,implies(implies(X,X_203),X_203))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X),implies(implies(X,X_203),X_203))) ),[0],$fot(implies(X,implies(implies(X,X_203),X_203)))]]) ).
cnf(refute_0_80,plain,
( ~ theorem(or(not(X),implies(implies(X,X_203),X_203)))
| theorem(implies(X,implies(implies(X,X_203),X_203))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(implies(X,X_203),X_203)),implies(X,implies(implies(X,X_203),X_203))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
theorem(implies(X,implies(implies(X,X_203),X_203))),
inference(resolve,[$cnf( theorem(or(not(X),implies(implies(X,X_203),X_203))) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
theorem(implies(X_272,implies(implies(X_272,X_273),X_273))),
inference(subst,[],[refute_0_81:[bind(X,$fot(X_272)),bind(X_203,$fot(X_273))]]) ).
cnf(refute_0_83,plain,
( ~ theorem(X_272)
| theorem(implies(implies(X_272,X_273),X_273)) ),
inference(resolve,[$cnf( theorem(implies(X_272,implies(implies(X_272,X_273),X_273))) )],[refute_0_82,refute_0_67]) ).
cnf(refute_0_84,plain,
( ~ theorem(not(not(or(X_290,not(X_290)))))
| theorem(implies(implies(not(not(or(X_290,not(X_290)))),X_3251),X_3251)) ),
inference(subst,[],[refute_0_83:[bind(X_272,$fot(not(not(or(X_290,not(X_290)))))),bind(X_273,$fot(X_3251))]]) ).
cnf(refute_0_85,plain,
theorem(implies(implies(not(not(or(X_290,not(X_290)))),X_3251),X_3251)),
inference(resolve,[$cnf( theorem(not(not(or(X_290,not(X_290))))) )],[refute_0_66,refute_0_84]) ).
cnf(refute_0_86,plain,
theorem(implies(implies(not(not(or(X_22111,not(X_22111)))),X_22112),X_22112)),
inference(subst,[],[refute_0_85:[bind(X_290,$fot(X_22111)),bind(X_3251,$fot(X_22112))]]) ).
cnf(refute_0_87,plain,
( ~ theorem(implies(not(not(or(X_22111,not(X_22111)))),X_22112))
| theorem(X_22112) ),
inference(resolve,[$cnf( theorem(implies(implies(not(not(or(X_22111,not(X_22111)))),X_22112),X_22112)) )],[refute_0_86,refute_0_0]) ).
cnf(refute_0_88,plain,
( ~ theorem(implies(not(not(or(X_22111,not(X_22111)))),implies(not(implies(X_121446,X_121447)),implies(X_121445,not(X_121447)))))
| theorem(implies(not(implies(X_121446,X_121447)),implies(X_121445,not(X_121447)))) ),
inference(subst,[],[refute_0_87:[bind(X_22112,$fot(implies(not(implies(X_121446,X_121447)),implies(X_121445,not(X_121447)))))]]) ).
cnf(refute_0_89,plain,
( ~ axiom(implies(or(X_13,X_14),or(X_14,X_13)))
| theorem(implies(or(X_13,X_14),or(X_14,X_13))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_13,X_14),or(X_14,X_13))))]]) ).
cnf(refute_0_90,plain,
axiom(implies(or(X_13,X_14),or(X_14,X_13))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_13)),bind(B,$fot(X_14))]]) ).
cnf(refute_0_91,plain,
theorem(implies(or(X_13,X_14),or(X_14,X_13))),
inference(resolve,[$cnf( axiom(implies(or(X_13,X_14),or(X_14,X_13))) )],[refute_0_90,refute_0_89]) ).
cnf(refute_0_92,plain,
( ~ theorem(implies(or(X_13,X_14),or(X_14,X_13)))
| ~ theorem(or(X_13,X_14))
| theorem(or(X_14,X_13)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_14,X_13))),bind(Y,$fot(or(X_13,X_14)))]]) ).
cnf(refute_0_93,plain,
( ~ theorem(or(X_13,X_14))
| theorem(or(X_14,X_13)) ),
inference(resolve,[$cnf( theorem(implies(or(X_13,X_14),or(X_14,X_13))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
( ~ theorem(or(implies(X_592,X_593),implies(X_591,not(X_593))))
| theorem(or(implies(X_591,not(X_593)),implies(X_592,X_593))) ),
inference(subst,[],[refute_0_93:[bind(X_13,$fot(implies(X_592,X_593))),bind(X_14,$fot(implies(X_591,not(X_593))))]]) ).
cnf(refute_0_95,plain,
( ~ theorem(implies(X_588,or(implies(X_589,X_590),not(X_590))))
| theorem(or(implies(X_589,X_590),implies(X_588,not(X_590)))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(X_588)),bind(X_47,$fot(implies(X_589,X_590))),bind(X_48,$fot(not(X_590)))]]) ).
cnf(refute_0_96,plain,
theorem(implies(X_7,or(not(X),X_7))),
inference(subst,[],[refute_0_9:[bind(X_3,$fot(X_7)),bind(X_4,$fot(not(X)))]]) ).
cnf(refute_0_97,plain,
implies(X,X_7) = or(not(X),X_7),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_7))]]) ).
cnf(refute_0_98,plain,
( implies(X,X_7) != or(not(X),X_7)
| or(not(X),X_7) = implies(X,X_7) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(implies(X,X_7))),bind(Y0,$fot(or(not(X),X_7)))]]) ).
cnf(refute_0_99,plain,
or(not(X),X_7) = implies(X,X_7),
inference(resolve,[$cnf( $equal(implies(X,X_7),or(not(X),X_7)) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
( or(not(X),X_7) != implies(X,X_7)
| ~ theorem(implies(X_7,or(not(X),X_7)))
| theorem(implies(X_7,implies(X,X_7))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(X_7,or(not(X),X_7))) ),[0,1],$fot(implies(X,X_7))]]) ).
cnf(refute_0_101,plain,
( ~ theorem(implies(X_7,or(not(X),X_7)))
| theorem(implies(X_7,implies(X,X_7))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_7),implies(X,X_7)) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
theorem(implies(X_7,implies(X,X_7))),
inference(resolve,[$cnf( theorem(implies(X_7,or(not(X),X_7))) )],[refute_0_96,refute_0_101]) ).
cnf(refute_0_103,plain,
theorem(implies(X_68,implies(X,X_68))),
inference(subst,[],[refute_0_102:[bind(X_7,$fot(X_68))]]) ).
cnf(refute_0_104,plain,
( ~ theorem(X_68)
| ~ theorem(implies(X_68,implies(X,X_68)))
| theorem(implies(X,X_68)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X,X_68))),bind(Y,$fot(X_68))]]) ).
cnf(refute_0_105,plain,
( ~ theorem(X_68)
| theorem(implies(X,X_68)) ),
inference(resolve,[$cnf( theorem(implies(X_68,implies(X,X_68))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
( ~ theorem(or(implies(X_293,X_294),not(X_294)))
| theorem(implies(X,or(implies(X_293,X_294),not(X_294)))) ),
inference(subst,[],[refute_0_105:[bind(X_68,$fot(or(implies(X_293,X_294),not(X_294))))]]) ).
cnf(refute_0_107,plain,
theorem(implies(X_289,implies(X,X_289))),
inference(subst,[],[refute_0_102:[bind(X_7,$fot(X_289))]]) ).
cnf(refute_0_108,plain,
( ~ theorem(implies(X_289,implies(X,X_289)))
| theorem(or(implies(X,X_289),not(X_289))) ),
inference(subst,[],[refute_0_52:[bind(X_17,$fot(X_289)),bind(X_18,$fot(implies(X,X_289)))]]) ).
cnf(refute_0_109,plain,
theorem(or(implies(X,X_289),not(X_289))),
inference(resolve,[$cnf( theorem(implies(X_289,implies(X,X_289))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
theorem(or(implies(X_293,X_294),not(X_294))),
inference(subst,[],[refute_0_109:[bind(X,$fot(X_293)),bind(X_289,$fot(X_294))]]) ).
cnf(refute_0_111,plain,
theorem(implies(X,or(implies(X_293,X_294),not(X_294)))),
inference(resolve,[$cnf( theorem(or(implies(X_293,X_294),not(X_294))) )],[refute_0_110,refute_0_106]) ).
cnf(refute_0_112,plain,
theorem(implies(X_588,or(implies(X_589,X_590),not(X_590)))),
inference(subst,[],[refute_0_111:[bind(X,$fot(X_588)),bind(X_293,$fot(X_589)),bind(X_294,$fot(X_590))]]) ).
cnf(refute_0_113,plain,
theorem(or(implies(X_589,X_590),implies(X_588,not(X_590)))),
inference(resolve,[$cnf( theorem(implies(X_588,or(implies(X_589,X_590),not(X_590)))) )],[refute_0_112,refute_0_95]) ).
cnf(refute_0_114,plain,
theorem(or(implies(X_592,X_593),implies(X_591,not(X_593)))),
inference(subst,[],[refute_0_113:[bind(X_588,$fot(X_591)),bind(X_589,$fot(X_592)),bind(X_590,$fot(X_593))]]) ).
cnf(refute_0_115,plain,
theorem(or(implies(X_591,not(X_593)),implies(X_592,X_593))),
inference(resolve,[$cnf( theorem(or(implies(X_592,X_593),implies(X_591,not(X_593)))) )],[refute_0_114,refute_0_94]) ).
cnf(refute_0_116,plain,
( ~ theorem(implies(or(X_5625,X_5624),or(X_5625,not(not(X_5624)))))
| ~ theorem(or(X_5625,X_5624))
| theorem(or(X_5625,not(not(X_5624)))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_5625,not(not(X_5624))))),bind(Y,$fot(or(X_5625,X_5624)))]]) ).
cnf(refute_0_117,plain,
theorem(implies(X_5621,not(not(X_5621)))),
inference(subst,[],[refute_0_62:[bind(X,$fot(X_5621))]]) ).
cnf(refute_0_118,plain,
( ~ axiom(implies(implies(X_34,X_35),implies(or(X_36,X_34),or(X_36,X_35))))
| theorem(implies(implies(X_34,X_35),implies(or(X_36,X_34),or(X_36,X_35)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_34,X_35),implies(or(X_36,X_34),or(X_36,X_35)))))]]) ).
cnf(refute_0_119,plain,
axiom(implies(implies(X_34,X_35),implies(or(X_36,X_34),or(X_36,X_35)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_34)),bind(B,$fot(X_35)),bind(C,$fot(X_36))]]) ).
cnf(refute_0_120,plain,
theorem(implies(implies(X_34,X_35),implies(or(X_36,X_34),or(X_36,X_35)))),
inference(resolve,[$cnf( axiom(implies(implies(X_34,X_35),implies(or(X_36,X_34),or(X_36,X_35)))) )],[refute_0_119,refute_0_118]) ).
cnf(refute_0_121,plain,
( ~ theorem(implies(X_34,X_35))
| ~ theorem(implies(implies(X_34,X_35),implies(or(X_36,X_34),or(X_36,X_35))))
| theorem(implies(or(X_36,X_34),or(X_36,X_35))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(or(X_36,X_34),or(X_36,X_35)))),bind(Y,$fot(implies(X_34,X_35)))]]) ).
cnf(refute_0_122,plain,
( ~ theorem(implies(X_34,X_35))
| theorem(implies(or(X_36,X_34),or(X_36,X_35))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_34,X_35),implies(or(X_36,X_34),or(X_36,X_35)))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
( ~ theorem(implies(X_5621,not(not(X_5621))))
| theorem(implies(or(X_5623,X_5621),or(X_5623,not(not(X_5621))))) ),
inference(subst,[],[refute_0_122:[bind(X_34,$fot(X_5621)),bind(X_35,$fot(not(not(X_5621)))),bind(X_36,$fot(X_5623))]]) ).
cnf(refute_0_124,plain,
theorem(implies(or(X_5623,X_5621),or(X_5623,not(not(X_5621))))),
inference(resolve,[$cnf( theorem(implies(X_5621,not(not(X_5621)))) )],[refute_0_117,refute_0_123]) ).
cnf(refute_0_125,plain,
theorem(implies(or(X_5625,X_5624),or(X_5625,not(not(X_5624))))),
inference(subst,[],[refute_0_124:[bind(X_5621,$fot(X_5624)),bind(X_5623,$fot(X_5625))]]) ).
cnf(refute_0_126,plain,
( ~ theorem(or(X_5625,X_5624))
| theorem(or(X_5625,not(not(X_5624)))) ),
inference(resolve,[$cnf( theorem(implies(or(X_5625,X_5624),or(X_5625,not(not(X_5624))))) )],[refute_0_125,refute_0_116]) ).
cnf(refute_0_127,plain,
( ~ theorem(or(implies(X_591,not(X_593)),implies(X_592,X_593)))
| theorem(or(implies(X_591,not(X_593)),not(not(implies(X_592,X_593))))) ),
inference(subst,[],[refute_0_126:[bind(X_5624,$fot(implies(X_592,X_593))),bind(X_5625,$fot(implies(X_591,not(X_593))))]]) ).
cnf(refute_0_128,plain,
theorem(or(implies(X_591,not(X_593)),not(not(implies(X_592,X_593))))),
inference(resolve,[$cnf( theorem(or(implies(X_591,not(X_593)),implies(X_592,X_593))) )],[refute_0_115,refute_0_127]) ).
cnf(refute_0_129,plain,
( ~ theorem(implies(or(X_4738,X_4739),implies(X_4740,or(X_4739,X_4738))))
| ~ theorem(or(X_4738,X_4739))
| theorem(implies(X_4740,or(X_4739,X_4738))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_4740,or(X_4739,X_4738)))),bind(Y,$fot(or(X_4738,X_4739)))]]) ).
cnf(refute_0_130,plain,
( ~ theorem(implies(or(X_13,X_14),or(X_14,X_13)))
| theorem(implies(X_91,implies(or(X_13,X_14),or(X_14,X_13)))) ),
inference(subst,[],[refute_0_105:[bind(X,$fot(X_91)),bind(X_68,$fot(implies(or(X_13,X_14),or(X_14,X_13))))]]) ).
cnf(refute_0_131,plain,
theorem(implies(X_91,implies(or(X_13,X_14),or(X_14,X_13)))),
inference(resolve,[$cnf( theorem(implies(or(X_13,X_14),or(X_14,X_13))) )],[refute_0_91,refute_0_130]) ).
cnf(refute_0_132,plain,
theorem(implies(X_4729,implies(or(X_13,X_14),or(X_14,X_13)))),
inference(subst,[],[refute_0_131:[bind(X_91,$fot(X_4729))]]) ).
cnf(refute_0_133,plain,
( ~ axiom(implies(or(X_56,implies(X_55,X_57)),implies(X_55,or(X_56,X_57))))
| theorem(implies(or(X_56,implies(X_55,X_57)),implies(X_55,or(X_56,X_57)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_56,implies(X_55,X_57)),implies(X_55,or(X_56,X_57)))))]]) ).
cnf(refute_0_134,plain,
axiom(implies(or(X_31,or(not(X),X_33)),or(not(X),or(X_31,X_33)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_31)),bind(B,$fot(not(X))),bind(C,$fot(X_33))]]) ).
cnf(refute_0_135,plain,
implies(X,or(X_31,X_33)) = or(not(X),or(X_31,X_33)),
inference(subst,[],[implies_definition:[bind(Y,$fot(or(X_31,X_33)))]]) ).
cnf(refute_0_136,plain,
( implies(X,or(X_31,X_33)) != or(not(X),or(X_31,X_33))
| or(not(X),or(X_31,X_33)) = implies(X,or(X_31,X_33)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(implies(X,or(X_31,X_33)))),bind(Y0,$fot(or(not(X),or(X_31,X_33))))]]) ).
cnf(refute_0_137,plain,
or(not(X),or(X_31,X_33)) = implies(X,or(X_31,X_33)),
inference(resolve,[$cnf( $equal(implies(X,or(X_31,X_33)),or(not(X),or(X_31,X_33))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
( or(not(X),or(X_31,X_33)) != implies(X,or(X_31,X_33))
| ~ axiom(implies(or(X_31,or(not(X),X_33)),or(not(X),or(X_31,X_33))))
| axiom(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(X_31,or(not(X),X_33)),or(not(X),or(X_31,X_33)))) ),[0,1],$fot(implies(X,or(X_31,X_33)))]]) ).
cnf(refute_0_139,plain,
( ~ axiom(implies(or(X_31,or(not(X),X_33)),or(not(X),or(X_31,X_33))))
| axiom(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33)))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_31,X_33)),implies(X,or(X_31,X_33))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
axiom(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33)))),
inference(resolve,[$cnf( axiom(implies(or(X_31,or(not(X),X_33)),or(not(X),or(X_31,X_33)))) )],[refute_0_134,refute_0_139]) ).
cnf(refute_0_141,plain,
or(not(X),X_33) = implies(X,X_33),
inference(subst,[],[refute_0_25:[bind(Y,$fot(X_33))]]) ).
cnf(refute_0_142,plain,
or(X_31,or(not(X),X_33)) = or(X_31,or(not(X),X_33)),
introduced(tautology,[refl,[$fot(or(X_31,or(not(X),X_33)))]]) ).
cnf(refute_0_143,plain,
( or(X_31,or(not(X),X_33)) != or(X_31,or(not(X),X_33))
| or(not(X),X_33) != implies(X,X_33)
| or(X_31,or(not(X),X_33)) = or(X_31,implies(X,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_31,or(not(X),X_33)),or(X_31,or(not(X),X_33))) ),[1,1],$fot(implies(X,X_33))]]) ).
cnf(refute_0_144,plain,
( or(not(X),X_33) != implies(X,X_33)
| or(X_31,or(not(X),X_33)) = or(X_31,implies(X,X_33)) ),
inference(resolve,[$cnf( $equal(or(X_31,or(not(X),X_33)),or(X_31,or(not(X),X_33))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
or(X_31,or(not(X),X_33)) = or(X_31,implies(X,X_33)),
inference(resolve,[$cnf( $equal(or(not(X),X_33),implies(X,X_33)) )],[refute_0_141,refute_0_144]) ).
cnf(refute_0_146,plain,
implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))) = implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))),
introduced(tautology,[refl,[$fot(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))))]]) ).
cnf(refute_0_147,plain,
( implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))) != implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33)))
| or(X_31,or(not(X),X_33)) != or(X_31,implies(X,X_33))
| implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))) = implies(or(X_31,implies(X,X_33)),implies(X,or(X_31,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))),implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33)))) ),[1,0],$fot(or(X_31,implies(X,X_33)))]]) ).
cnf(refute_0_148,plain,
( or(X_31,or(not(X),X_33)) != or(X_31,implies(X,X_33))
| implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))) = implies(or(X_31,implies(X,X_33)),implies(X,or(X_31,X_33))) ),
inference(resolve,[$cnf( $equal(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))),implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33)))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))) = implies(or(X_31,implies(X,X_33)),implies(X,or(X_31,X_33))),
inference(resolve,[$cnf( $equal(or(X_31,or(not(X),X_33)),or(X_31,implies(X,X_33))) )],[refute_0_145,refute_0_148]) ).
cnf(refute_0_150,plain,
( implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))) != implies(or(X_31,implies(X,X_33)),implies(X,or(X_31,X_33)))
| ~ axiom(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))))
| axiom(implies(or(X_31,implies(X,X_33)),implies(X,or(X_31,X_33)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33)))) ),[0],$fot(implies(or(X_31,implies(X,X_33)),implies(X,or(X_31,X_33))))]]) ).
cnf(refute_0_151,plain,
( ~ axiom(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))))
| axiom(implies(or(X_31,implies(X,X_33)),implies(X,or(X_31,X_33)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33))),implies(or(X_31,implies(X,X_33)),implies(X,or(X_31,X_33)))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
axiom(implies(or(X_31,implies(X,X_33)),implies(X,or(X_31,X_33)))),
inference(resolve,[$cnf( axiom(implies(or(X_31,or(not(X),X_33)),implies(X,or(X_31,X_33)))) )],[refute_0_140,refute_0_151]) ).
cnf(refute_0_153,plain,
axiom(implies(or(X_56,implies(X_55,X_57)),implies(X_55,or(X_56,X_57)))),
inference(subst,[],[refute_0_152:[bind(X,$fot(X_55)),bind(X_31,$fot(X_56)),bind(X_33,$fot(X_57))]]) ).
cnf(refute_0_154,plain,
theorem(implies(or(X_56,implies(X_55,X_57)),implies(X_55,or(X_56,X_57)))),
inference(resolve,[$cnf( axiom(implies(or(X_56,implies(X_55,X_57)),implies(X_55,or(X_56,X_57)))) )],[refute_0_153,refute_0_133]) ).
cnf(refute_0_155,plain,
theorem(implies(or(not(X),implies(X_58,X_60)),implies(X_58,or(not(X),X_60)))),
inference(subst,[],[refute_0_154:[bind(X_55,$fot(X_58)),bind(X_56,$fot(not(X))),bind(X_57,$fot(X_60))]]) ).
cnf(refute_0_156,plain,
implies(X,X_60) = or(not(X),X_60),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_60))]]) ).
cnf(refute_0_157,plain,
( implies(X,X_60) != or(not(X),X_60)
| or(not(X),X_60) = implies(X,X_60) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(implies(X,X_60))),bind(Y0,$fot(or(not(X),X_60)))]]) ).
cnf(refute_0_158,plain,
or(not(X),X_60) = implies(X,X_60),
inference(resolve,[$cnf( $equal(implies(X,X_60),or(not(X),X_60)) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
( or(not(X),X_60) != implies(X,X_60)
| ~ theorem(implies(or(not(X),implies(X_58,X_60)),implies(X_58,or(not(X),X_60))))
| theorem(implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),implies(X_58,X_60)),implies(X_58,or(not(X),X_60)))) ),[0,1,1],$fot(implies(X,X_60))]]) ).
cnf(refute_0_160,plain,
( ~ theorem(implies(or(not(X),implies(X_58,X_60)),implies(X_58,or(not(X),X_60))))
| theorem(implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_60),implies(X,X_60)) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
theorem(implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),implies(X_58,X_60)),implies(X_58,or(not(X),X_60)))) )],[refute_0_155,refute_0_160]) ).
cnf(refute_0_162,plain,
or(not(X),implies(X_58,X_60)) = implies(X,implies(X_58,X_60)),
inference(subst,[],[refute_0_25:[bind(Y,$fot(implies(X_58,X_60)))]]) ).
cnf(refute_0_163,plain,
implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60))) = implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60))),
introduced(tautology,[refl,[$fot(implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60))))]]) ).
cnf(refute_0_164,plain,
( implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60))) != implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60)))
| or(not(X),implies(X_58,X_60)) != implies(X,implies(X_58,X_60))
| implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60))) = implies(implies(X,implies(X_58,X_60)),implies(X_58,implies(X,X_60))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60))),implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60)))) ),[1,0],$fot(implies(X,implies(X_58,X_60)))]]) ).
cnf(refute_0_165,plain,
( or(not(X),implies(X_58,X_60)) != implies(X,implies(X_58,X_60))
| implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60))) = implies(implies(X,implies(X_58,X_60)),implies(X_58,implies(X,X_60))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60))),implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60)))) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60))) = implies(implies(X,implies(X_58,X_60)),implies(X_58,implies(X,X_60))),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_58,X_60)),implies(X,implies(X_58,X_60))) )],[refute_0_162,refute_0_165]) ).
cnf(refute_0_167,plain,
( implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60))) != implies(implies(X,implies(X_58,X_60)),implies(X_58,implies(X,X_60)))
| ~ theorem(implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60))))
| theorem(implies(implies(X,implies(X_58,X_60)),implies(X_58,implies(X,X_60)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60)))) ),[0],$fot(implies(implies(X,implies(X_58,X_60)),implies(X_58,implies(X,X_60))))]]) ).
cnf(refute_0_168,plain,
( ~ theorem(implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60))))
| theorem(implies(implies(X,implies(X_58,X_60)),implies(X_58,implies(X,X_60)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60))),implies(implies(X,implies(X_58,X_60)),implies(X_58,implies(X,X_60)))) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
theorem(implies(implies(X,implies(X_58,X_60)),implies(X_58,implies(X,X_60)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),implies(X_58,X_60)),implies(X_58,implies(X,X_60)))) )],[refute_0_161,refute_0_168]) ).
cnf(refute_0_170,plain,
( ~ theorem(implies(X,implies(X_58,X_60)))
| ~ theorem(implies(implies(X,implies(X_58,X_60)),implies(X_58,implies(X,X_60))))
| theorem(implies(X_58,implies(X,X_60))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_58,implies(X,X_60)))),bind(Y,$fot(implies(X,implies(X_58,X_60))))]]) ).
cnf(refute_0_171,plain,
( ~ theorem(implies(X,implies(X_58,X_60)))
| theorem(implies(X_58,implies(X,X_60))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,implies(X_58,X_60)),implies(X_58,implies(X,X_60)))) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
( ~ theorem(implies(X_4729,implies(or(X_13,X_14),or(X_14,X_13))))
| theorem(implies(or(X_13,X_14),implies(X_4729,or(X_14,X_13)))) ),
inference(subst,[],[refute_0_171:[bind(X,$fot(X_4729)),bind(X_58,$fot(or(X_13,X_14))),bind(X_60,$fot(or(X_14,X_13)))]]) ).
cnf(refute_0_173,plain,
theorem(implies(or(X_13,X_14),implies(X_4729,or(X_14,X_13)))),
inference(resolve,[$cnf( theorem(implies(X_4729,implies(or(X_13,X_14),or(X_14,X_13)))) )],[refute_0_132,refute_0_172]) ).
cnf(refute_0_174,plain,
theorem(implies(or(X_4738,X_4739),implies(X_4740,or(X_4739,X_4738)))),
inference(subst,[],[refute_0_173:[bind(X_13,$fot(X_4738)),bind(X_14,$fot(X_4739)),bind(X_4729,$fot(X_4740))]]) ).
cnf(refute_0_175,plain,
( ~ theorem(or(X_4738,X_4739))
| theorem(implies(X_4740,or(X_4739,X_4738))) ),
inference(resolve,[$cnf( theorem(implies(or(X_4738,X_4739),implies(X_4740,or(X_4739,X_4738)))) )],[refute_0_174,refute_0_129]) ).
cnf(refute_0_176,plain,
( ~ theorem(or(implies(X_591,not(X_593)),not(not(implies(X_592,X_593)))))
| theorem(implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593))))) ),
inference(subst,[],[refute_0_175:[bind(X_4738,$fot(implies(X_591,not(X_593)))),bind(X_4739,$fot(not(not(implies(X_592,X_593))))),bind(X_4740,$fot(X_121362))]]) ).
cnf(refute_0_177,plain,
theorem(implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593))))),
inference(resolve,[$cnf( theorem(or(implies(X_591,not(X_593)),not(not(implies(X_592,X_593))))) )],[refute_0_128,refute_0_176]) ).
cnf(refute_0_178,plain,
or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593))) = implies(not(implies(X_592,X_593)),implies(X_591,not(X_593))),
inference(subst,[],[refute_0_25:[bind(X,$fot(not(implies(X_592,X_593)))),bind(Y,$fot(implies(X_591,not(X_593))))]]) ).
cnf(refute_0_179,plain,
implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593)))) = implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593)))),
introduced(tautology,[refl,[$fot(implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593)))))]]) ).
cnf(refute_0_180,plain,
( implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593)))) != implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593))))
| or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593))) != implies(not(implies(X_592,X_593)),implies(X_591,not(X_593)))
| implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593)))) = implies(X_121362,implies(not(implies(X_592,X_593)),implies(X_591,not(X_593)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593)))),implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593))))) ),[1,1],$fot(implies(not(implies(X_592,X_593)),implies(X_591,not(X_593))))]]) ).
cnf(refute_0_181,plain,
( or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593))) != implies(not(implies(X_592,X_593)),implies(X_591,not(X_593)))
| implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593)))) = implies(X_121362,implies(not(implies(X_592,X_593)),implies(X_591,not(X_593)))) ),
inference(resolve,[$cnf( $equal(implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593)))),implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593))))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593)))) = implies(X_121362,implies(not(implies(X_592,X_593)),implies(X_591,not(X_593)))),
inference(resolve,[$cnf( $equal(or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593))),implies(not(implies(X_592,X_593)),implies(X_591,not(X_593)))) )],[refute_0_178,refute_0_181]) ).
cnf(refute_0_183,plain,
( implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593)))) != implies(X_121362,implies(not(implies(X_592,X_593)),implies(X_591,not(X_593))))
| ~ theorem(implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593)))))
| theorem(implies(X_121362,implies(not(implies(X_592,X_593)),implies(X_591,not(X_593))))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593))))) ),[0],$fot(implies(X_121362,implies(not(implies(X_592,X_593)),implies(X_591,not(X_593)))))]]) ).
cnf(refute_0_184,plain,
( ~ theorem(implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593)))))
| theorem(implies(X_121362,implies(not(implies(X_592,X_593)),implies(X_591,not(X_593))))) ),
inference(resolve,[$cnf( $equal(implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593)))),implies(X_121362,implies(not(implies(X_592,X_593)),implies(X_591,not(X_593))))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
theorem(implies(X_121362,implies(not(implies(X_592,X_593)),implies(X_591,not(X_593))))),
inference(resolve,[$cnf( theorem(implies(X_121362,or(not(not(implies(X_592,X_593))),implies(X_591,not(X_593))))) )],[refute_0_177,refute_0_184]) ).
cnf(refute_0_186,plain,
theorem(implies(not(not(or(X_22111,not(X_22111)))),implies(not(implies(X_121446,X_121447)),implies(X_121445,not(X_121447))))),
inference(subst,[],[refute_0_185:[bind(X_121362,$fot(not(not(or(X_22111,not(X_22111)))))),bind(X_591,$fot(X_121445)),bind(X_592,$fot(X_121446)),bind(X_593,$fot(X_121447))]]) ).
cnf(refute_0_187,plain,
theorem(implies(not(implies(X_121446,X_121447)),implies(X_121445,not(X_121447)))),
inference(resolve,[$cnf( theorem(implies(not(not(or(X_22111,not(X_22111)))),implies(not(implies(X_121446,X_121447)),implies(X_121445,not(X_121447))))) )],[refute_0_186,refute_0_88]) ).
cnf(refute_0_188,plain,
theorem(implies(not(implies(p,q)),implies(not(p),not(q)))),
inference(subst,[],[refute_0_187:[bind(X_121445,$fot(not(p))),bind(X_121446,$fot(p)),bind(X_121447,$fot(q))]]) ).
cnf(refute_0_189,plain,
$false,
inference(resolve,[$cnf( theorem(implies(not(implies(p,q)),implies(not(p),not(q)))) )],[refute_0_188,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL206-3 : TPTP v8.1.0. Bugfixed v2.4.1.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 03:00:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 261.84/262.04 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 261.84/262.04
% 261.84/262.04 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 261.84/262.06
%------------------------------------------------------------------------------